Feynman-Kac formulae



There is a mathematically rich theory about particle filters work. The notoriously abstruse Del Moral (2004); Doucet, Freitas, and Gordon (2001) are universally commended for unifying and making consistent the diffusion processes and Feynman-Kac formulae and “propagation of chaos”. I will get around to them eventually, maybe?

References

Cérou, F., P. Del Moral, T. Furon, and A. Guyader. 2011. “Sequential Monte Carlo for Rare Event Estimation.” Statistics and Computing 22 (3): 795–808. https://doi.org/10.1007/s11222-011-9231-6.
Chopin, Nicolas, and Omiros Papaspiliopoulos. 2020. An Introduction to Sequential Monte Carlo. Springer Series in Statistics. Springer International Publishing. https://doi.org/10.1007/978-3-030-47845-2.
Chuang, Howard Jen-Hao. 2010. “The Feynman-Kac Formula:Relationships Between Stochastic DifferentialEquations and Partial Differential Equations.” Honours, ANU. https://maths-intranet.anu.edu.au/MSIonly/honours_theses/2010/Howard_Chuang.pdf.
Del Moral, Pierre. 2004. Feynman-Kac Formulae: Genealogical and Interacting Particle Systems with Applications. 2004 edition. Latheronwheel, Caithness: Springer.
Del Moral, Pierre, and Arnaud Doucet. 2010. “Interacting Markov Chain Monte Carlo Methods for Solving Nonlinear Measure-Valued Equations.” The Annals of Applied Probability 20 (2): 593–639. https://doi.org/10.1214/09-AAP628.
Del Moral, Pierre, Peng Hu, and Liming Wu. 2011. On the Concentration Properties of Interacting Particle Processes. Vol. 3. Now Publishers. https://doi.org/10.1561/2200000026.
Del Moral, Pierre, and Laurent Miclo. 2000. “Branching and Interacting Particle Systems Approximations of Feynman-Kac Formulae with Applications to Non-Linear Filtering.” In Séminaire de Probabilités XXXIV, 1–145. Lecture Notes in Mathematics 1729. Springer. https://doi.org/10.1007/BFb0103798.
Doucet, Arnaud, Nando Freitas, and Neil Gordon. 2001. Sequential Monte Carlo Methods in Practice. New York, NY: Springer New York. http://public.eblib.com/choice/publicfullrecord.aspx?p=3087052.
Doucet, Arnaud, Simon Godsill, and Christophe Andrieu. 2000. “On Sequential Monte Carlo Sampling Methods for Bayesian Filtering.” Statistics and Computing 10 (3, 3): 197–208. https://doi.org/10.1023/A:1008935410038.
Nualart, David, and Wim Schoutens. 2001. “Backward Stochastic Differential Equations and Feynman-Kac Formula for Lévy Processes, with Applications in Finance.” Bernoulli 7 (5): 761–76. https://projecteuclid.org/euclid.bj/1079399541.
Papanicolaou, Andrew. 2019. “Introduction to Stochastic Differential Equations (SDEs) for Finance.” January 2, 2019. http://arxiv.org/abs/1504.05309.

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